Note that the above cost function is constraint-free and differentiable [1]}, albeit nonconvex. To deal with nonconvexity, we propose to optimise the expectation of \(\widetilde{\mathcal {W}}_2^2\big (\nu ^{\mathcal {G}_1, g} , \nu ^{\mathcal {G}_2, g}_{\mathcal {B}(P)} \big )\)  w.r.t. the parameters \(\theta \)  of some distribution \(p_\theta \) , that is
\(\operatornamewithlimits{minimize}_{\theta } \; \underbrace{\mathbb {E}_{P\sim p_\theta }\big \lbrace  \widetilde{\mathcal {W}}_2^2\big (\nu ^{\mathcal {G}_1, g} , \nu ^{\mathcal {G}_2, g}_{\mathcal {B}(P)} \big ) \big \rbrace }_{U(\theta )}.\) 
